The barrier layer of copper interconnects plays a crucial role in preventing diffusion between copper and dielectric materials. These barrier materials must meet specific requirements, including high stability, strong adhesion to copper and dielectric materials, and low resistance. Since the 1990s, tantalum nitride/tantalum (TaN/Ta) has been commonly used as copper barrier layers and liner layers. However, as continuous developments in integrated chip scaling occur, the impact of interconnect delay on chip speed has become increasingly significant. The high resistivity and inability of TaN/Ta to electroplate directly the copper have made it challenge to meet the evolving demands. In this paper, the recent advancements in copper interconnect barrier materials, including metal alloys, self-assembled molecular layers (SAM), two-dimensional materials and high-entropy alloys, were reviewed. Additionally, this paper highlighted the challenges and suggest future research directions.